Long, a former machine gunner who served in Afghanistan, opened fire with a handgun in the attack, then apparently killed himself as scores of police officers closed in.
FBI investigators following leads in quest to investigate the gunman's state of mind.
Investigators have not commented on a motive for the rampage or whether mental illness played a role.
Among the 12 victims are Ventura County Sheriff's Deputy Ron Helus, a 29-year veteran of the force who was the first to arrive on the scene, as well as actress Tamera Mowry-Housley's niece, 18-year-old Pepperdine student Alaina Housley.
Kuredjian said there is no timeline for completing the investigation.
A survivor of last year's Las Vegas shooting died in Wednesday's attack in California, according to multiple news reports.
Last year, a country music festival in Las Vegas was the scene of the worst mass shooting in modern U.S. history. I want gun control. No.
Guardiola raises prospect of new action over City finances
David Silva is usually the man but this time I think it's time for Raheem Sterling to step up in a huge game. We asked our Soccer Saturday pundits who they think will be each team's most important player on Sunday.
After the ceremony, she said she's most upset that the bloodshed is now affecting where she lives. "You're always overanalyzing people, trying to figure out if something were to go down, 'What would I do?"' Kelly said Borderline had become a safe haven for dozens of Vegas survivors: "It is our home".
At the White House, Trump touted his efforts to fund work on PTSD among veterans. I want gun control.
The incident happened in April, when yelling and loud banging noises coming from the home Long shared with his mother prompted a next-door neighbour to call authorities. "We offer our deepest condolences to the Manrique family and ask that our Eagles around the world join us in keeping all those impacted by this tragedy in your thoughts and prayers". "I suspected he had a gun there because I heard a gunshot one night, over a year ago".
"It's nearly like we haven't had enough time to process how we feel", she said in a phone interview, describing a head-spinning shift from a tear-filled vigil to fielding calls from friends and relatives in need of help after receiving evacuation orders.
Asked what made him decide to go back and help others, he added: 'Instinct, that's all that I could do. "The last thing I said was, 'Son, I love you.' That was the last thing I said".
The people of Thousand Oaks had barely recovered from a deadly bar shooting that claimed 12 lives, including that of a police officer, before the "worst fire since 1982" spread in populated parts of the city forcing thousands into their cars in search of temporary accommodation or emergency shelters.
Mourners cry and comfort each other during a vigil for the victims of the Thousand Oaks shooting.
He and his wife, who have lived in Thousand Oaks for 34 years, took refuge in a nearby shopping center before returning to their home later on Friday. Associated Press writers Rebecca Boone in Boise, Idaho, and Christopher Weber in Thousand Oaks, contributed.